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/* blas/source_tbsv_c.h
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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{
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const int conj = (TransA == CblasConjTrans) ? -1 : 1;
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const int Trans = (TransA != CblasConjTrans) ? TransA : CblasTrans;
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const int nonunit = (Diag == CblasNonUnit);
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INDEX i, j;
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CHECK_ARGS10(TBSV,order,Uplo,TransA,Diag,N,K,A,lda,X,incX);
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if (N == 0)
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return;
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/* form x := inv( A )*x */
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if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasUpper)
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|| (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasLower)) {
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INDEX ix = OFFSET(N, incX) + incX * (N - 1);
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for (i = N; i > 0 && i--;) {
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BASE tmp_real = REAL(X, ix);
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BASE tmp_imag = IMAG(X, ix);
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const INDEX j_min = i + 1;
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const INDEX j_max = GSL_MIN(N, i + K + 1);
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INDEX jx = OFFSET(N, incX) + j_min * incX;
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for (j = j_min; j < j_max; j++) {
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const BASE Aij_real = CONST_REAL(A, lda * i + (j - i));
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const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + (j - i));
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const BASE x_real = REAL(X, jx);
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const BASE x_imag = IMAG(X, jx);
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tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
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tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
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jx += incX;
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}
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if (nonunit) {
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const BASE a_real = CONST_REAL(A, lda * i + 0);
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const BASE a_imag = conj * CONST_IMAG(A, lda * i + 0);
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const BASE s = xhypot(a_real, a_imag);
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const BASE b_real = a_real / s;
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const BASE b_imag = a_imag / s;
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REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
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IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
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} else {
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REAL(X, ix) = tmp_real;
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IMAG(X, ix) = tmp_imag;
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}
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ix -= incX;
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}
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} else if ((order == CblasRowMajor && Trans == CblasNoTrans && Uplo == CblasLower)
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|| (order == CblasColMajor && Trans == CblasTrans && Uplo == CblasUpper)) {
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/* forward substitution */
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INDEX ix = OFFSET(N, incX);
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for (i = 0; i < N; i++) {
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BASE tmp_real = REAL(X, ix);
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BASE tmp_imag = IMAG(X, ix);
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const INDEX j_min = (K > i ? 0 : i - K);
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const INDEX j_max = i;
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INDEX jx = OFFSET(N, incX) + j_min * incX;
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for (j = j_min; j < j_max; j++) {
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const BASE Aij_real = CONST_REAL(A, lda * i + (K + j - i));
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const BASE Aij_imag = conj * CONST_IMAG(A, lda * i + (K + j - i));
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const BASE x_real = REAL(X, jx);
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const BASE x_imag = IMAG(X, jx);
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tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
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tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
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jx += incX;
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}
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if (nonunit) {
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const BASE a_real = CONST_REAL(A, lda * i + K);
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const BASE a_imag = conj * CONST_IMAG(A, lda * i + K);
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const BASE s = xhypot(a_real, a_imag);
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const BASE b_real = a_real / s;
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const BASE b_imag = a_imag / s;
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REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
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IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
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} else {
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REAL(X, ix) = tmp_real;
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IMAG(X, ix) = tmp_imag;
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}
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ix += incX;
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}
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} else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasUpper)
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|| (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasLower)) {
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/* form x := inv( A' )*x */
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/* forward substitution */
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INDEX ix = OFFSET(N, incX);
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for (i = 0; i < N; i++) {
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BASE tmp_real = REAL(X, ix);
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BASE tmp_imag = IMAG(X, ix);
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const INDEX j_min = (K > i ? 0 : i - K);
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const INDEX j_max = i;
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INDEX jx = OFFSET(N, incX) + j_min * incX;
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for (j = j_min; j < j_max; j++) {
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const BASE Aij_real = CONST_REAL(A, (i - j) + lda * j);
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const BASE Aij_imag = conj * CONST_IMAG(A, (i - j) + lda * j);
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const BASE x_real = REAL(X, jx);
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const BASE x_imag = IMAG(X, jx);
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tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
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tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
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jx += incX;
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}
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if (nonunit) {
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const BASE a_real = CONST_REAL(A, 0 + lda * i);
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const BASE a_imag = conj * CONST_IMAG(A, 0 + lda * i);
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const BASE s = xhypot(a_real, a_imag);
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const BASE b_real = a_real / s;
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const BASE b_imag = a_imag / s;
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REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
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IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
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} else {
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REAL(X, ix) = tmp_real;
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IMAG(X, ix) = tmp_imag;
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}
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ix += incX;
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}
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} else if ((order == CblasRowMajor && Trans == CblasTrans && Uplo == CblasLower)
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|| (order == CblasColMajor && Trans == CblasNoTrans && Uplo == CblasUpper)) {
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/* backsubstitution */
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INDEX ix = OFFSET(N, incX) + incX * (N - 1);
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for (i = N; i > 0 && i--;) {
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BASE tmp_real = REAL(X, ix);
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BASE tmp_imag = IMAG(X, ix);
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const INDEX j_min = i + 1;
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const INDEX j_max = GSL_MIN(N, i + K + 1);
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INDEX jx = OFFSET(N, incX) + j_min * incX;
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for (j = j_min; j < j_max; j++) {
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const BASE Aij_real = CONST_REAL(A, (K + i - j) + lda * j);
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const BASE Aij_imag = conj * CONST_IMAG(A, (K + i - j) + lda * j);
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const BASE x_real = REAL(X, jx);
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const BASE x_imag = IMAG(X, jx);
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tmp_real -= Aij_real * x_real - Aij_imag * x_imag;
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tmp_imag -= Aij_real * x_imag + Aij_imag * x_real;
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jx += incX;
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}
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if (nonunit) {
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const BASE a_real = CONST_REAL(A, K + lda * i);
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const BASE a_imag = conj * CONST_IMAG(A, K + lda * i);
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const BASE s = xhypot(a_real, a_imag);
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const BASE b_real = a_real / s;
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const BASE b_imag = a_imag / s;
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REAL(X, ix) = (tmp_real * b_real + tmp_imag * b_imag) / s;
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IMAG(X, ix) = (tmp_imag * b_real - tmp_real * b_imag) / s;
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} else {
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REAL(X, ix) = tmp_real;
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IMAG(X, ix) = tmp_imag;
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}
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ix -= incX;
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}
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} else {
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BLAS_ERROR("unrecognized operation");
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}
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}
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